In a clock, a large gear completes a rotation every 45 seconds, a small gear completes a rotation every 18 seconds. the gears aligned now, how many seconds will pass before the gears are in line again?

90 seconds will pass before the gears are in line again

Step-by-step explanation:

In a clock, a large gear completes a rotation every 45 seconds.

The small gear completes a rotation every 18 seconds.

To get the number of seconds needed so these both will pass before the gears are in line again, we will simply find the LCM of 45 and 18.

45 = 3 x 3 x 5

18 = 2 x 3 x 3

LCM = 2 x 3 x 3 x 5 = 90

Hence, 90 seconds will pass before the gears are in line again